KC Sinha Mathematics Solution Class 11 Chapter 32 Probability Exercise 32.3

 Exercise 32.3

Page no 32.49

Type 1

Question 1

If $E$ and $F$ are two events associated with a random experiment such that $P(F)=0.35, P(E$ or $F)=0.85$ and $P(E$ and $F)=0.5$, find $P(E)$.

Question 2

$A$ and $B$ are two mutually exclusive events of an experiment. If $P$ (not $A$ ) $=065, P(A \cup B)=065$ and $P(B)=p$, find the value of $p$.

Question 3

If $P(A)=\frac{3}{8}, P(B)=\frac{1}{3}$ and $P(A \cap B)=\frac{1}{4}$, then find $P(A \cup B)$ and $P\left(A^{\prime} \cap B^{\prime}\right)$.

Question 4

The probability that a student will pass in Mathematics is $\frac{3}{5}$ and the probability that he will pass in English is $\frac{1}{3}$. If the probability that he will pass in both Mathematics and English is $\frac{1}{8}$, what is the probability that he will pass in at least one subject ?

Question 5

The probability of two events $A$ and $B$ are $0.25$ and $0.50$ respectively. The probability of their simultaneous occurrence is 0.14. Find the probability that neither $A$ nor $B$ occurs.

Question 6

$A$ and $B$ are two events such that $P(A)=0.42, P(B)=0.48$ and $P(A$ and $B)=0.16$ Determine

(i) $P(A$ or $B)$

(ii) $P(A$ but not $B)$

(iii) $P(B$ but not $A)$

(iv) $P$ (neither $A$ nor $B$ )

Question 7

Events $A$ and $B$ are such that $P(A)=\frac{1}{2}, P(B)=\frac{7}{12}$ and $P($ not $A$ or not $B)=\frac{1}{9}$. State whether $A$ and $B$ are mutually exclusive.

Question 8

$A, B, C$ are three mutually exclusive and exhaustive events associated with a random experiment. Find $P(A)$, if $P(B)=\frac{3}{4} P(A)$ and $P(C)=\frac{1}{3} P(B)$.

Question 9

100 students appeared for two examinations. 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has passed at least one examination.

Question 10

Given $P(A)=\frac{3}{5}$ and $P(B)=\frac{1}{5}$. Find $P(A$ or $B)$, if $A$ and $B$ are mutually exclusive events.

Question 11

Events $E$ and $F$ are such that $P$ (not $E$ or not $F$ ) $=0.25$, State whether $E$ and $F$ are mutually exclusive.

Question 12

Fill in the blanks in following table :

$\begin{array}{lccc}P(A) & P(B) & P(A \cap B) & P(A \cup B) \\ \text { (i) } \frac{1}{3} & \frac{1}{5} & \frac{1}{15} & \ldots \\ \text { (ii) } 0.35 & \ldots . . & 0.25 & 0.6 \\ \text { (iii) } 0.5 & 0.35 & \ldots & 0.7\end{array}$

Page no 32.50

Question 13

If E and F are events such that $P(E)=\frac{1}{4}, P(F)=\frac{1}{2}$ and $P(E$ and $F)=\frac{1}{8}$, find (i) $P(E$ or $F)$   (ii) $P(\operatorname{not} E$ and not $F)$

Question 14

$A$ and $B$ are events such that $P(A)=042, P(B)=(4+8$ and $P(A$ and $B)=016$ Determine (i) $P(\operatorname{not} A)$. (ii) $P(\operatorname{not} B)$ and

(iii) $P(A$ or $B)$

Question 15

 In Class XI of a school $40 \%$ of the students study Mathematics  and $30 \%$ study Biology. $10 \%$ of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.

Question 16

The probability that a student will pass the final examination in both English and Hindi is $0.5$ and the probability of passing neither is $0.1$. If the probability of passing the English examination is $0.75$, what is the probability of passing the Hindi examination ?

Question 17

In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is $0.8$ and the probability of passing the second examination is $0.7$. The probability of passing atleast one of them is $0.95$. What is the probability of passing both ?

Type 2

Question 18

Two dice are thrown together once. Find the probability of getting an even number on the first dice or a total of 8 .

Question 19

One number is chosen from numbers 1 to 200 . Find the probability that it is divisible by 4 or 6 ?

Question 20

A natural number is chosen at random from among the first 500 . What is the probability that the number so chosen is divisible by 3 or 5 ?

Question 21

Two dice are rolled once. Find the probability that

(i) the numbers on the two dice are different

(ii) the total is at least 3

(iii) the total is 6

(iv) the total is 7 or 9

(v) neither a doublet nor a total of 9 appear.

Question 22

A card is drawn from a pack of 52 cards. Find the probability of getting an ace or a club or a red card.

Question 23

A die is thrown twice. What is the probability that at least one of the two throws come up with the number 4 ?

Question 24

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a spade or a king.

Question 25

One ticket is drawn at random out of 30 tickets numbered from 1 to 30 . Find the probability that the number on the ticket is a multiple of 5 or 7 .

Question 26

A drawer contains 50 bolts and 150 nuts. Half of the bolts and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is rusted or a bolt.

Question 27

If the odds against winning a race of three horses are respectively $3: 1,4: 1$ and $5: 1$, what is the probability that one of these horses will win ?